Maureen McCormick actually did date Marcia's celebrity crush, Desi Arnaz Jr., several years after this episode was filmed.
Although the question of where the Bradys live is definitively answered (Los Angeles) in Welcome Aboard (1974), this episode contains several clues. Some of the street names (Riverside, Vineland) and bookstore names (The Valley Book Emporium) reflect the Bradys living in 'the Valley' (the San Fernando Valley of LA). Also, Alice's casual remark about knowing Lucille Ball's housekeeper, and the fact that Desi Arnaz Jr can just drop by to visit, all imply that they're in LA.
In TV reruns, this is usually shown as the final episode of the first season. The final episode of the season was actually Lost Locket, Found Locket.
The title is based on the song "The Impossible Dream," composed by Mitch Leigh, with lyrics written by Joe Darion, for the 1965 musical, "Man of La Mancha." The song is performed by Richard Kiley, and was a hit for many other singers in the 1960s. The original stage production opened at the ANTA Washington Square theater, in New York City, on 22 November 1965, moving to Broadway after a short run, and eventually having a total of 2,329 performances. "Man of La Mancha" won the 1966 Tony Awards for the Best Musical and Best Score.